Sigma and Pi Bonds

A sigma bond results from orbitals overlapping directly along the line joining the two nuclei. That head-on arrangement maximizes overlap, so sigma bonds are strong, and electron density is concentrated between the nuclei. Every bond between two atoms contains exactly one sigma bond, whether it is single, double or triple.

The internuclear axis is the line joining the bonded nuclei. A σ interaction has electron density with cylindrical symmetry about that axis. It can arise from s–s overlap, s–hybrid overlap or appropriate head-on overlap of p or hybrid orbitals. “Sigma” therefore describes overlap symmetry, not one particular kind of atomic orbital. In a normal localized single/double/triple bond between a pair of atoms, there is one σ component.

In the simple second-period valence-bond model, parallel unhybridized p orbitals overlap side-on. The π bonding density lies on both sides of a nodal plane that contains the internuclear axis. A p orbital's two lobes belong to one orbital; the density above and below the plane forms one π component, not two separate π bonds.

Side-on overlap is usually less effective than the corresponding head-on overlap, so a π component is generally weaker than a comparable σ component. A double bond is nevertheless stronger overall than a related single bond because it contains both components. This is not a universal prediction of which bond breaks first in every reaction; reaction pathways and products matter. Other orbital models describe delocalized and metal π bonding, so “only sp or sp² atoms can ever π-bond” is too broad outside this local model.

In ethyne, H-C triple bond C-H, each carbon is sp. There are two C-H sigma bonds, one C-C sigma bond and two C-C pi bonds, for three sigma and two pi bonds in total. In benzene, each of the six carbons is sp² with one p orbital, and those six p orbitals overlap around the ring in a delocalized pi system.

For HC≡CH, the carbon–carbon σ bond is sp–sp overlap. Each C–H σ bond is carbon sp overlapping hydrogen 1s. Two perpendicular pairs of unhybridized carbon p orbitals form the two C–C π components. Thus there are three σ and two π bonds in the whole molecule, while the C≡C link itself contains one σ and two π. Always state whether a count concerns one link or the whole molecule.

In benzene, all six carbons have one p orbital, and these form a delocalized π system across the ring. A Kekulé drawing counts three π bonds for bookkeeping, but they are not three permanently isolated double bonds with independent long/short positions.

For propene CH₃–CH=CH₂, six C–H connections contribute six σ bonds, and two C–C connections contribute two more, totaling eight σ. The one double bond contributes one π. Include hydrogens implied by a condensed or skeletal formula, and count each connection once rather than once from each atom. For a ring, include the closing bond too. A useful audit is that replacing a single connection by a double connection adds one π without adding another σ direction.